Processing method and processing device for concave-convex gear

ABSTRACT

A trajectory extracting step of extracting a relative movement trajectory of each convex tooth pin of a mating gear with respect to a concave-convex gear at the time when torque is transmitted between the mating gear (fixed shaft) and the concave-convex gear (nutation gear) and a machining step of, when the concave-convex gear is machined on a concave tooth forming face of a disc-shaped workpiece on which the concave teeth have not been machined, moving at least one of the disc-shaped workpiece and a working tool such that a relative movement trajectory of the working tool with respect to the disc-shaped workpiece coincides with the relative movement trajectory of each convex tooth pin with respect to the concave-convex gear, extracted in the trajectory extracting step, are included.

TECHNICAL FIELD

The invention relates to a machining method and machining device for aconcave-convex gear.

BACKGROUND ART

There is a nutation gear set as one of reduction gears. The nutationgear set is, for example, described in Patent Document 1. That is, thenutation gear set is formed of a first gear, a second gear and an inputshaft that have the same rotation central axis, and a nutation gear thatperforms differential rotation with respect to the first gear and thesecond gear while wobbling therebetween. The nutation gear is supportedby the input shaft so as to be rotatable about an inclined rotationcentral axis. Furthermore, the inclined rotation central axis relativelyrotates about the rotation central axis of the first gear with therotation of the input shaft. By so doing, the nutation gear wobbles withrespect to the first gear and the second gear. Then, first nutationteeth that mesh with the first gear are formed on a face of the nutationgear, adjacent to the first gear, and second nutation teeth that meshwith the second gear are formed on a face of the nutation gear, adjacentto the second gear. Then, as the nutation gear wobbles, differentialrotation occurs between the first gear and the nutation gear or betweenthe second gear and the nutation gear. That is, when the second gear isset as an output shaft with respect to the input shaft, speed may bereduced at a large reduction gear ratio.

The nutation gear has an extremely complex meshing face that meshes withthe first gear or the second gear, so machining is not easy. A machiningdevice for the nutation gear is, for example, described in PatentDocument 1.

PRIOR ART DOCUMENT Patent Document

Patent Document 1: Japanese Patent Application Publication No.2006-272497

SUMMARY OF THE INVENTION Problem to be Solved by the Invention

Incidentally, various machining methods of machining gears, such as aspur gear and a bevel gear, have been proposed and implemented.Machining of a nutation gear is also implemented using a special purposemachine as described in Patent Document 1; however, a special machiningdevice is used or a special technique is required, so it is notconsidered to be easy.

The invention is contemplated in view of such a situation, and it is anobject of the invention to provide a new machining method and machiningdevice for a concave-convex gear.

Means for Solving the Problem

In order to solve the above problem, the invention extracts a relativemovement trajectory between each convex tooth of a mating gear and acorresponding one of concave teeth of a concave-convex gear that is amachining target at the time of differential rotation and then moves aworking tool and a disc-shaped workpiece such that a relative movementtrajectory between the working tool and the disc-shaped workpiececoincides with the extracted relative movement trajectory between eachconvex tooth of the mating gear and the concave-convex gear at the timeof machining the concave teeth of the concave-convex gear on thedisc-shaped workpiece.

A feature of the invention according to claim 1 provides a machiningmethod for a concave-convex gear, concave teeth of the concave-convexgear and convex teeth of a mating gear being continuously formed in acircumferential direction, and the concave teeth meshing with the convexteeth of the mating gear to allow torque transmission to or from themating gear. The machining method includes:

a trajectory extracting step of extracting a relative movementtrajectory of each convex tooth of the mating gear with respect to theconcave-convex gear that serves as a machining target at the time whentorque is transmitted between the mating gear and the concave-convexgear; and

a machining step of, when the concave teeth of the concave-convex gearare machined on a concave tooth forming face of a disc-shaped workpiecethat is the concave-convex gear on which the concave teeth have not beenmachined, moving at least one of the disc-shaped workpiece and a workingtool such that a relative movement trajectory of the working tool withrespect to the disc-shaped workpiece coincides with the relativemovement trajectory of each convex tooth of the mating gear with respectto the concave-convex gear, extracted in the trajectory extracting step.

A feature of the invention according to claim 2 is such that, in claim1, the concave-convex gear is a gear that rotates about an intersectingaxis that intersects with a rotation central axis of the mating gear. Afeature of the invention according to claim 3 is such that, in claim 1or 2, the number of the convex teeth of the mating gear is differentfrom the number of the concave teeth of the concave-convex gear. Afeature of the invention according to claim 4 is such that, in any oneof claims 1 to 3, in the trajectory extracting step, a relative movementtrajectory of a reference axis of each convex tooth of the mating gearwith respect to the concave-convex gear is extracted, and the referenceaxis is an axis that is parallel to a line of intersection of a tooththickness central plane and reference conical surface of each convextooth of the mating gear.

A feature of the invention according to claim 5 is such that, in any oneof claims 1 to 4, the mating gear includes a mating gear body that isintegrally formed with the convex teeth or the mating gear body that isseparately formed from the convex teeth and that supports the convexteeth, and a sectional shape of an outer peripheral surface of eachconvex tooth of the mating gear in a direction orthogonal to a referenceaxis of the convex tooth is formed in a circular arc shape.

A feature of the invention according to claim 6 is such that, in claim5, the working tool is a disc-shaped tool, and, in the machining step,each convex tooth of the mating gear is spuriously expressed by thedisc-shaped tool through infeed operation at multiple portions at whicha central axis of the disc-shaped tool is shifted in a tooth groovedirection of a corresponding one of the concave teeth of theconcave-convex gear to machine the concave teeth of the concave-convexgear with the disc-shaped tool.

A feature of the invention according to claim 7 is such that, in claim6, the machining method includes:

a simulation step of performing machining simulation by moving at leastone of the disc-shaped workpiece and the working tool; and

a cutting position calculation step of comparing a preset ideal shapemodel with a shape of a result of the machining simulation to calculatea position of infeed operation by shifting the central axis of thedisc-shaped tool in the tooth groove direction of each concave tooth ofthe concave-convex gear, wherein

in the machining step, the concave teeth of the concave-convex gear aremachined on the basis of the position of infeed operation, calculated inthe cutting position calculation step.

A feature of the invention according to claim 8 is such that, in claim7, in the cutting position calculation step, the position of the infeedoperation is calculated so that a machining time is minimized while adeviation between the shape of the result of the machining simulationand the ideal shape model is smaller than or equal to a set permissiblevalue.

A feature of the invention according to claim 9 is such that, in claim5, the working tool is formed in a pin shape that is coincident with orsimilar to an outer peripheral shape of each convex tooth of the matinggear and that rotates about a pin central axis. A feature of theinvention according to claim 10 is such that, in claim 5, the workingtool is a circulating belt-shaped tool and has a straight portion in acirculating direction.

A feature of the invention according to claim 11 is such that, in anyone of claims 1 to 10, the machining method includes a coordinateconversion step of calculating a movement trajectory of the working toolin a workpiece coordinate system by subjecting the relative movementtrajectory of each convex tooth with respect to the concave-convex gear,extracted in the trajectory extracting step, to coordinate conversion,and

in the machining step, at least one of the disc-shaped workpiece and theworking tool is moved on the basis of the movement trajectory of theworking tool, calculated in the coordinate conversion step.

A feature of the invention according to claim 12 is such that, in claim11, the concave-convex gear is a gear that rotates about an intersectingaxis that intersects with a rotation central axis of the mating gear,

a sectional shape of an outer peripheral surface of each convex tooth ofthe mating gear in a direction orthogonal to a reference axis of theconvex tooth is formed in a circular arc shape,

a relative movement trajectory of each convex tooth of the mating gearwith respect to the concave-convex gear, extracted in the trajectoryextracting step, is decomposed into:

a first linear axis along which a reference position of the convex toothof the mating gear is moved in a direction orthogonal to a plane that istangent to a concave tooth forming face of the disc-shaped workpiece;

a second linear axis along which the reference position of the convextooth of the mating gear is moved in a tooth groove direction of acorresponding one of the concave teeth of the concave-convex gear in theplane that is tangent to the concave tooth forming face of thedisc-shaped workpiece;

a third linear axis along which the reference position of the convextooth of the mating gear is moved in a direction orthogonal to thesecond linear axis in the plane that is tangent to the concave toothforming face of the disc-shaped workpiece;

a fourth rotation axis along which the reference position of the convextooth of the mating gear is rotated about the first linear axis;

a fifth rotation axis along which the reference position of the convextooth of the mating gear is rotated about the third linear axis; and

a sixth indexing axis that coincides with a rotation central axis of theconcave-convex gear and that indexes a rotation phase of theconcave-convex gear, in the coordinate conversion step, the relativemovement trajectory of each convex tooth of the mating gear, expressedby the first linear axis, the third linear axis, the fourth rotationaxis, the fifth rotation axis and the sixth indexing axis when movementof the reference position of the convex tooth of the mating gear alongthe second linear axis is assumed to be performed along the third linearaxis is calculated in the case where it is presumed that a tooth lengthof each convex tooth of the mating gear is infinite, and

in the machining step, at least one of the disc-shaped workpiece and theworking tool is moved on the basis of the calculated relative movementtrajectory.

A feature of the invention according to claim 13 is such that, in claim11, the concave-convex gear is a gear that rotates about an intersectingaxis that intersects with a rotation central axis of the mating gear,

a sectional shape of an outer peripheral surface of each convex tooth ofthe mating gear in a direction orthogonal to a reference axis of theconvex tooth is formed in a circular arc shape,

a relative movement trajectory of each convex tooth of the mating gearwith respect to the concave-convex gear, extracted in the trajectoryextracting step, is decomposed into:

a first linear axis along which a reference position of the convex toothof the mating gear is moved in a direction orthogonal to a plane that istangent to a concave tooth forming face of the disc-shaped workpiece;

a second linear axis along which the reference position of the convextooth of the mating gear is moved in a tooth groove direction of acorresponding one of the concave teeth of the concave-convex gear in theplane that is tangent to the concave tooth forming face of thedisc-shaped workpiece;

a third linear axis along which the reference position of the convextooth of the mating gear is moved in a direction orthogonal to thesecond linear axis in the plane that is tangent to the concave toothforming face of the disc-shaped workpiece;

a fourth rotation axis along which the reference position of the convextooth of the mating gear is rotated about the first linear axis;

a fifth rotation axis along which the reference position of the convextooth of the mating gear is rotated about the third linear axis; and

a sixth indexing axis that coincides with a rotation central axis of theconcave-convex gear and that indexes a rotation phase of theconcave-convex gear,

in the coordinate conversion step, the relative movement trajectory ofeach convex tooth of the mating gear, expressed by the first linearaxis, the second linear axis, the fourth rotation axis, the fifthrotation axis and the sixth indexing axis when movement of the referenceposition of the convex tooth of the mating gear along the third linearaxis is assumed to be performed along the second linear axis iscalculated in the case where it is presumed that a tooth length of eachconvex tooth of the mating gear is infinite, and

in the machining step, at least one of the disc-shaped workpiece and theworking tool is moved on the basis of the calculated relative movementtrajectory.

A feature of the invention according to claim 14 is such that, in claim11, the concave-convex gear is a gear that rotates about an intersectingaxis that intersects with a rotation central axis of the mating gear,

a sectional shape of an outer peripheral surface of each convex tooth ofthe mating gear in a direction orthogonal to a reference axis of theconvex tooth is formed in a circular arc shape,

a relative movement trajectory of each convex tooth of the mating gearwith respect to the concave-convex gear, extracted in the trajectoryextracting step, is decomposed into:

a first linear axis along which a reference position of the convex toothof the mating gear is moved in a direction orthogonal to a plane that istangent to a concave tooth forming face of the disc-shaped workpiece;

a second linear axis along which the reference position of the convextooth of the mating gear is moved in a tooth groove direction of acorresponding one of the concave teeth of the concave-convex gear in theplane that is tangent to the concave tooth forming face of thedisc-shaped workpiece;

a third linear axis along which the reference position of the convextooth of the mating gear is moved in a direction orthogonal to thesecond linear axis in the plane that is tangent to the concave toothforming face of the disc-shaped workpiece;

a fourth rotation axis along which the reference position of the convextooth of the mating gear is rotated about the first linear axis;

a fifth rotation axis along which the reference position of the convextooth of the mating gear is rotated about the third linear axis; and

a sixth indexing axis that coincides with a rotation central axis of theconcave-convex gear and that indexes a rotation phase of theconcave-convex gear,

in the coordinate conversion step, the relative movement trajectory ofeach convex tooth of the mating gear, expressed by the first linearaxis, the second linear axis, the third linear axis, the fourth rotationaxis and the sixth indexing axis is calculated by decomposing movementof the reference position of the convex tooth of the mating gear alongthe fifth rotation axis into movement along the first linear axis andmovement along the second linear axis, and

in the machining step, at least one of the disc-shaped workpiece and theworking tool is moved on the basis of the calculated relative movementtrajectory.

A feature of the invention according to claim 15 is such that, in claim11, the concave-convex gear is a gear that rotates about an intersectingaxis that intersects with a rotation central axis of the mating gear,

a sectional shape of an outer peripheral surface of each convex tooth ofthe mating gear in a direction orthogonal to a reference axis of theconvex tooth is formed in a circular arc shape,

a relative movement trajectory of each convex tooth of the mating gearwith respect to the concave-convex gear, extracted in the trajectoryextracting step, is decomposed into:

a first linear axis along which a reference position of the convex toothof the mating gear is moved in a direction orthogonal to a plane that istangent to a concave tooth forming face of the disc-shaped workpiece;

a second linear axis along which the reference position of the convextooth of the mating gear is moved in a tooth groove direction of acorresponding one of the concave teeth of the concave-convex gear in theplane that is tangent to the concave tooth forming face of thedisc-shaped workpiece;

a third linear axis along which the reference position of the convextooth of the mating gear is moved in a direction orthogonal to thesecond linear axis in the plane that is tangent to the concave toothforming face of the disc-shaped workpiece;

a fourth rotation axis along which the reference position of the convextooth of the mating gear is rotated about the first linear axis;

a fifth rotation axis along which the reference position of the convextooth of the mating gear is rotated about the third linear axis; and

a sixth indexing axis that coincides with a rotation central axis of theconcave-convex gear and that indexes a rotation phase of theconcave-convex gear,

in the coordinate conversion step, the relative movement trajectory ofeach convex tooth of the mating gear, expressed by the first linearaxis, the second linear axis, the third linear axis, the fifth rotationaxis and the sixth indexing axis when the fourth rotation axis isbrought into coincidence with the sixth indexing axis is calculated, and

in the machining step, at least one of the disc-shaped workpiece and theworking tool is moved on the basis of the calculated relative movementtrajectory.

A feature of the invention according to claim 16 provides a machiningdevice for a concave-convex gear in which concave teeth and convex teethare continuously formed in a circumferential direction and the concaveteeth mesh with convex teeth of a mating gear to allow torquetransmission to or from the mating gear. The machining device includes:

trajectory extracting means for extracting a relative movementtrajectory of each convex tooth of the mating gear with respect to theconcave-convex gear that serves as a machining target at the time whentorque is transmitted between the mating gear and the concave-convexgear; and

machining means for, when the concave teeth of the concave-convex gearare machined on a concave tooth forming face of a disc-shaped workpiecethat is the concave-convex gear on which the concave teeth have not beenmachined, moving at least one of the disc-shaped workpiece and a workingtool such that a relative movement trajectory of the working tool withrespect to the disc-shaped workpiece coincides with the relativemovement trajectory of each convex tooth of the mating gear with respectto the concave-convex gear, extracted in the trajectory extracting step.

Advantageous Effects of the Invention

With the invention according to claim 1 configured as described above,an NC machine tool is used to make it possible to machine the concaveteeth of the concave-convex gear. That is, the same NC machine tool maybe used to machine concave-convex gears having various shapes.Specifically, an NC program is generated on the basis of the relativemovement trajectory extracted in the trajectory extracting step, and theconcave teeth of the concave-convex gear may be machined in themachining step using the NC program. In this way, it is possible toextremely easily machine the concave teeth of the concave-convex gear.

Here, in the concave-convex gear that rotates about an intersecting axiswith respect to a mating gear (hereinafter, also referred to as“concave-convex gear with an intersecting axis”), the meshing rate ofthe mating gear and the concave-convex gear increases. Therefore, it ispossible to reduce size, increase strength and achieve quietness. On theother hand, in order to achieve desirable tooth contact, it is requiredto form a tooth flank shape having an extremely high accuracy, so thereis a problem that machining of a tooth flank shape is not easy. Incontrast to this, with the invention according to claim 2, the concaveteeth of the concave-convex gear with an intersecting axis may be easilyand highly accurately formed. As a result, according to the invention,it is possible to reduce machining cost in the case of accuracyequivalent to the existing art. Note that, other than the concave-convexgear with an intersecting axis, the invention may be applied to aconcave-convex gear with a parallel axis, that is, a so-called spurgear.

With the invention according to claim 3, because the number of teeth ofthe mating gear is different from the number of teeth of theconcave-convex gear, so it is configured such that torque istransmittable while the mating gear and the concave-convex gear performdifferential rotation. Then, because the number of teeth is differenttherebetween, the shape of each concave tooth of the concave-convex gearis an extremely complex shape. In such a case as well, by applying theinvention, it is possible to reliably machine the concave teeth of theconcave-convex gear. Note that, when the number of teeth of the matinggear is equal to the number of teeth of the concave-convex gear, thatis, when torque is transmitted while rotating at the same number ofrevolutions as well, the machining method according to the invention is,of course, applicable.

With the invention according to claim 4, although the relative movementbetween the concave-convex gear and the mating gear is three-dimensionalcomplex movement, the reference axis is used to make it possible toreliably understand the relative movement trajectory. Here, thereference conical surface is a surface that passes through the referencepitch circle of each cross section. The case where a cone angle of 0° ora cone angle of 180° is included. In addition, the tooth thicknesscentral plane of each convex tooth of the mating gear means the centralplane of each convex tooth in a circumferential width.

With the invention according to claim 5, the sectional shape of eachconvex tooth of the mating gear in the direction orthogonal to thereference axis is a circular arc shape. By so doing, the mating gear andthe concave-convex gear are able to extremely smoothly transmit torque.On the other hand, machining of the concave teeth of the concave-convexgear becomes complicated. Because the sectional shape of each convextooth of the mating gear in the direction orthogonal to the referenceaxis is a circular arc shape, each concave tooth of the concave-convexgear has a sectional shape approximate to a circular arc concave shapeas a whole, and, specifically, has a sectional shape of which theopening edge portions of the circular arc concave shape are sagged. Inthis way, even when each concave tooth of the concave-convex gear has acomplex shape, the invention is applied to make it possible to reliablyand highly accurately perform machining. As a result, it is possible toform the nutation gear 15 having high performance at low cost. Notethat, even when each convex tooth of the mating gear is formed in ashape other than a pin shape, the machining method of the invention maybe applied.

With the invention according to claim 6, by using the disc-shaped toolto spuriously express a pin-shaped convex tooth, it is possible toreliably machine the concave teeth of the concave-convex gear.Furthermore, by using the disc-shaped tool, the stiffness of the toolmay be enhanced, so it is possible to perform machining with highaccuracy. With the invention according to claim 7, machining isperformed on the basis of the position of the infeed operation, obtainedthrough comparison between the ideal shape model and the simulationmodel, so it is possible to form the highly accurate concave teeth ofthe concave-convex gear.

With the invention according to claim 8, it is possible to calculate amachining condition with a shortest period of time while ensuringmachining accuracy within the permissible value. With the inventionaccording to claim 9, when the working tool has a shape that iscoincident with or similar to each convex tooth of the mating gear,movement of the working tool is set so as to be similar to that of eachconvex tooth of the mating gear to thereby make it possible to form theoptimal concave teeth of the concave-convex gear. With the inventionaccording to claim 10, it is possible to easily express each convextooth of the mating gear owing to the straight portion of thebelt-shaped tool. Thus, by setting movement of the straight portion ofthe belt-shaped tool so as to be similar to each convex tooth of themating gear, it is possible to form the optimal concave teeth of theconcave-convex gear.

With the invention according to claim 11, the relative movementtrajectory of each convex tooth of the mating gear is converted tomovement of the working tool in the workpiece coordinate system. Here,in the trajectory extracting step, the relative movement trajectory ofeach convex tooth of the mating gear with respect to the concave-convexgear at the time of torque transmission is extracted. Then, depending onthe type of working tool, the relative movement trajectory extracted inthe trajectory extracting step and the movement trajectory of theworking tool in the workpiece coordinate system differ from each other.That is, owing to the invention, the NC program based on the type ofworking tool may be generated.

With the invention according to claim 12, movement along the secondlinear axis is omitted to make it possible to allow machining with fiveaxes. With the invention according to claim 13, movement along the thirdlinear axis is omitted to make it possible to allow machining with fiveaxes. With the invention according to claim 14, the fifth rotation axisis omitted to make it possible to allow machining with five axes. Inthis case, the disc-shaped tool is desirably used as the working tool toform a spurious convex tooth of the mating gear. With the inventionaccording to claim 15, movement along the fourth rotation axis isomitted to make it possible to allow machining with five axes.

With the invention according to claim 16, similar advantageous effectsto those of the invention of the machining method according to claim 1are obtained. In addition, in the invention of the machining device, theabove described other features related to the machining method may alsobe applied as the machining device. In this case, similar advantageouseffects to the advantageous effects based on the respective features areobtained.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1( a) and FIG. 1( b) are axially sectional views of a nutation gearset. FIG. 1( a) shows a case where convex tooth pins are respectivelyseparately formed from a fixed shaft body and an output shaft body, andFIG. 1( b) shows a case where convex tooth pins are respectivelyintegrally formed with the fixed shaft body and the output shaft body.

FIG. 2( a) and FIG. 2( b) are enlarged views of a meshing portionbetween each convex tooth pin (convex tooth) and a nutation gear, andare views in an axial direction of the convex tooth pin. FIG. 2( a)shows a case where the convex tooth pin is separately formed from afixed shaft, and FIG. 2( b) shows a case where the convex tooth pin isintegrally formed with the fixed shaft.

FIG. 3 is a perspective view of each nutation concave tooth.

FIG. 4( a) is a view of each nutation concave tooth when viewed from aradially outer side of the nutation gear. FIG. 4( b) is a view of eachnutation concave tooth when viewed in a direction along a rotationcentral axis of the nutation gear.

FIG. 5 is a flow chart that shows processes in a first embodiment.

FIG. 6( a 1) to FIG. 6( c 2) are views that show relative movementsbetween each nutation concave tooth of the nutation gear and acorresponding one of the convex tooth pins (convex teeth). FIG. 6( a 1)is a view in the direction along the rotation central axis of thenutation gear in relative position between the convex tooth pin and thenutation concave tooth in a state before the convex tooth pin mesheswith the nutation concave tooth. FIG. 6( a 2) is a view from the rightside of FIG. 6( a 1). FIG. 6( b 1) is a view in the direction along therotation central axis of the nutation gear in relative position betweenthe convex tooth pin and the nutation concave tooth in a state where theconvex tooth pin is in mesh with the nutation concave tooth. FIG. 6( b2) is a view from the right side of FIG. 6( b 1). FIG. 6( c 1) is a viewin the direction along the rotation central axis of the nutation gear inrelative position between the convex tooth pin and the nutation concavetooth in a state where the convex tooth pin is separated from the meshedstate with the nutation concave tooth. FIG. 6( c 2) is a view from theright side of FIG. 6(c 1). In FIG. 6( a 1) to FIG. 6( c 2), thereference axis of the convex tooth pin (alternate long and short dashline in the longitudinal direction of the convex tooth pin) and thecentral position of the convex tooth pin (filled circle).

FIG. 7( a) is a view that shows the movement trajectory of the referenceaxis of the convex tooth pin and the movement trajectory of the centralposition of the convex tooth pin with respect to the nutation gear whenviewed in the direction along the rotation central axis of the nutationgear. FIG. 7( b) is a view that shows the movement trajectory of thereference axis of the convex tooth pin and the movement trajectory ofthe central position of the convex tooth pin with respect to thenutation gear when viewed in the radial direction of the nutation gear.Numeric characters in circles coincide with axis numbers.

FIG. 8( a) and FIG. 8( b) are views that show a toroidal grinding wheel(disc-shaped tool). FIG. 8( a) is a view of the toroidal grinding wheelwhen viewed in the direction along the rotation axis, and FIG. 8( b) isa view in the radial direction.

FIG. 9( a) and FIG. 9( b) show a circulating belt grinding wheel thatserves as a working tool, FIG. 9( a) is a view in the direction alongthe rotation axis of the circulating belt grinding wheel, and FIG. 9( b)is an A-A sectional view of FIG. 9( a).

FIG. 10( a) and FIG. 10( b) are views that illustrate a required axisconfiguration of a machine tool in the first embodiment. FIG. 10( a)shows the axis configuration of the machine tool in a plane parallel toa second linear axis and a third linear axis, and FIG. 10( b) shows theaxis configuration of the machine tool in a plane parallel to a firstlinear axis and the second linear axis. Numeric characters in circlescoincide with axis numbers.

FIG. 11 is an explanatory view in the case where movement along a fourthrotation axis is decomposed into movement along a sixth indexing axisand movement along the third linear axis in a second embodiment. Thatis, FIG. 11 is a view in the case where the central position of theconvex tooth pin is shifted onto the third linear axis.

FIG. 12 is an explanatory view in the case where movement along thefourth rotation axis is decomposed into movement along the sixthindexing axis and movement along the second linear axis in a thirdembodiment. That is, FIG. 12 is a view in the case where the centralposition of the convex tooth pin is shifted onto the second linear axis.

FIG. 13( a) and FIG. 13( b) are conceptual explanatory views in the casewhere movement along the second linear axis is decomposed into movementalong the first linear axis and movement along the third linear axis ina fourth embodiment. FIG. 13( a) is a view in the plane that passesthrough the second linear axis and the third linear axis. FIG. 13( b) isa view in the plane that passes through the first linear axis and thesecond linear axis.

FIG. 14( a) and FIG. 14( b) are conceptual explanatory views in the casewhere the central position of the convex tooth pin is decomposed intocomponents in the fourth embodiment. FIG. 14( a) is a view in the casewhere the central position of the convex tooth pin is decomposed into acomponent in the plane that passes through the second linear axis andthe third linear axis, and FIG. 14( b) is a view in the case where thecentral position of the convex tooth pin is decomposed into a componentin the plane that passes through the first linear axis and the secondlinear axis.

FIG. 15( a) and FIG. 15( b) are views that illustrate a required axisconfiguration of a machine tool in the fourth embodiment. FIG. 15( a)shows the axis configuration of the machine tool in the plane parallelto the second linear axis and the third linear axis, and FIG. 15( b)shows the axis configuration of the machine tool in the plane parallelto the first linear axis and the second linear axis. Numeric charactersin circles coincide with axis numbers.

FIG. 16( a) and FIG. 16( b) are conceptual explanatory views in the casewhere movement along the third linear axis is decomposed into movementalong the first linear axis and movement along the second linear axis ina fifth embodiment. FIG. 16( a) is a view in the plane that passesthrough the second linear axis and the third linear axis. FIG. 16( b) isa view in the plane that passes through the first linear axis and thesecond linear axis.

FIG. 17( a) and FIG. 17 are conceptual explanatory views in the casewhere the central position of the convex tooth pin is decomposed intocomponents in the fifth embodiment. FIG. 17( a) is a view in the casewhere the central position of the convex tooth pin is decomposed into acomponent in the plane that passes through the second linear axis andthe third linear axis, and FIG. 17( b) is a view in the case where thecentral position of the convex tooth pin is decomposed into a componentin the plane that passes through the first linear axis and the secondlinear axis.

FIG. 18( a) and FIG. 18( b) are views that illustrate a required axisconfiguration of a machine tool in the fifth embodiment. FIG. 18( a)shows the axis configuration of the machine tool in the plane parallelto the second linear axis and the third linear axis, and FIG. 18( b)shows the axis configuration of the machine tool in the plane parallelto the first linear axis and the second linear axis. Numeric charactersin circles coincide with axis numbers.

FIG. 19 is a view that shows movement of the rotation axis of thetoroidal grinding wheel in the plane parallel to the first linear axisand the second linear axis in a sixth embodiment.

FIG. 20( a) and FIG. 20( b) are views that show the machined shape of anutation concave tooth in the case where the toroidal grinding wheelundergoes infeed operation at one cutting position with respect to atooth groove direction of the nutation concave tooth in the sixthembodiment. FIG. 20( a) is a view in the direction along the rotationcentral axis of the nutation gear, FIG. 20( b) is a view from the rightside of FIG. 20( a).

FIG. 21 is an explanatory view in the case where the toroidal grindingwheel undergoes infeed operation at three cutting positions with respectto the tooth groove direction of the nutation concave tooth in the sixthembodiment.

FIG. 22 is a flow chart that shows processes in the sixth embodiment.

FIG. 23( a) and FIG. 23( b) are sectional views of a torque transmissiondevice formed of a concave-convex gear with an intersecting axis in aseventh embodiment. FIG. 23( a) shows a case where convex tooth pins areseparately formed from an input shaft body, and FIG. 23( b) shows a casewhere the convex tooth pins are integrally formed with the input shaftbody.

FIG. 24 is a view that shows convex teeth in another alternativeembodiment.

MODES FOR CARRYING OUT THE INVENTION

Hereinafter, specific embodiments of a machining method and machiningdevice for a concave-convex gear according to the invention will bedescribed with reference to the drawings. Here, a nutation gear set isformed of two pairs of the relationship between a concave-convex gearand a mating gear in the case where a rotation central axis of theconcave-convex gear intersects with a rotation central axis of themating gear. In the present embodiments, a machining method andmachining device for a nutation gear of a nutation gear set will bedescribed by way of example. Note that, in the following description, anutation gear corresponds to a “concave-convex gear” according to theinvention, and a fixed shaft 12 and an output shaft 13 each correspondto a “mating gear” according to the invention.

First Embodiment

Six-Axis Configuration (Three Linear Axes and Three Rotation Axes)

A machining method and machining device for a nutation gear of anutation gear set according to a first embodiment will be described withreference to FIG. 1 to FIG. 10. The machining device in the presentembodiment shows the case of a six-axis configuration having threeorthogonal linear axes and three rotation axes.

(1) Configuration of Nutation Gear Set

The configuration of the nutation gear set that uses the nutation gearthat is a machining object of the invention will be described withreference to FIG. 1 to FIG. 4. Here, FIG. 1( a) shows a case whereconvex tooth pins 12 b and 13 b are respectively separately formed froma fixed shaft body 12 a and an output shaft body 13 a, and FIG. 1( b)shows a case where the convex tooth pins 12 b and 13 b are respectivelyintegrally formed with the fixed shaft body 12 a and the output shaftbody 13 a. Note that, hereinafter, description will be made mainly withreference to FIG. 1( a), and FIG. 1( b) will be described in terms ofonly the difference from FIG. 1( a).

The nutation gear set is used as a reduction gear, and is able to obtainan extremely large reduction gear ratio. As shown in FIG. 1( a), thenutation gear set mainly includes an input shaft 11, a fixed shaft 12(that corresponds to a “mating gear” of the invention), an output shaft13 (that corresponds to a “mating gear” of the invention), an outer ring14, an inner ring 15 (that corresponds to a “concave-convex gear” of theinvention) and rolling elements 16.

The input shaft 11 constitutes a rotor of a motor (not shown), and is ashaft that rotates as the motor is driven. The input shaft has acylindrical shape, and rotates about a rotation central axis A (shown inFIG. 1( a)). An inclined surface 11 a is formed on the inner peripheralsurface of the input shaft 11. The inclined surface 11 a is acylindrical inner peripheral surface that has an axis B, inclined at aslight angle with respect to the rotation central axis A, as a centralaxis.

The fixed shaft 12 (that corresponds to the “mating gear” of theinvention) is fixed to a housing (not shown). The fixed shaft 12 isformed of the fixed shaft body 12 a and the plurality of convex toothpins 12 b. The fixed shaft body 12 a (that corresponds to a “mating gearbody” of the invention) is a cylindrical member having the axis A as arotation central axis. A plurality (G1) of the convex tooth pins 12 b(that correspond to “convex teeth of the mating gear” of the invention)are supported on an axial end face of the fixed shaft body 12 a at equalintervals in a circumferential direction of the rotation central axis A.Then, each of the convex tooth pins 12 b is formed in a circularcolumnar shape or a cylindrical shape, and both ends thereof aresupported by the fixed shaft body 12 a such that the convex tooth pins12 b are arranged radially. Furthermore, each of the convex tooth pins12 b is supported by the fixed shaft body 12 a so as to be rotatableabout an axis in an axial direction (reference axis direction) of theconvex tooth pin 12 b and in a radial direction of the fixed shaft body12 a. Furthermore, part of each convex tooth pin 12 b protrudes from theaxial end face of the fixed shaft body 12 a. That is, the fixed shaft 12functions as a gear having convex teeth of which the number of teeth isZ1.

In addition, in the above description, as shown in FIG. 1( a) and FIG.2( a), the convex tooth pins 12 b of the fixed shaft 12 are separatelyformed from the fixed shaft body 12 a, and are supported by the fixedshaft body 12 a. Other than this, as shown in

FIG. 1( b) and FIG. 2( b), the convex tooth pins 12 b may be integrallyformed with the fixed shaft body 12 a. In this case, the integrallyformed convex tooth pins 12 b, as well as the portions of the convextooth pins 12 b protruding from the axial end face of the fixed shaftbody 12 a in the separately formed case, protrude from the axial endface of a portion corresponding to the fixed shaft body 12 a.

The output shaft 13 (that corresponds to the “mating gear” of theinvention) is supported by the housing (not shown) so as to be rotatableabout the rotation central axis A, and is coupled to an output member(not shown). The output shaft 13 is formed of the output shaft body 13 aand the plurality of convex tooth pins 13 b. The output shaft body 13 a(that corresponds to a “mating gear body” of the invention) is acylindrical member having the axis A as a rotation central axis. Thatis, the output shaft body 13 a is provided coaxially with the inputshaft 11 and the fixed shaft body 12 a.

A plurality (G4) of the convex tooth pins 13 b (that correspond to“convex teeth of the mating gear” of the invention) are supported on anaxial end face of the output shaft body 13 a at equal intervals in thecircumferential direction of the rotation central axis A. Then, each ofthe convex tooth pins 13 b is formed in a circular columnar shape or acylindrical shape, and both ends thereof are supported by the outputshaft body 13 a such that convex tooth pins 13 b are arranged radially.Furthermore, each of the convex tooth pins 13 b is supported by theoutput shaft body 13 a so as to be rotatable about an axis in an axialdirection (reference axis direction) of the convex tooth pin 13 b and ina radial direction of the output shaft body 13 a. Furthermore, the axialend face of the output shaft body 13 a, supporting the convex tooth pins13 b, is provided so as to face and is spaced apart at a predetermineddistance in the axial direction from the axial end face of the fixedshaft body 12 a, supporting the convex tooth pins 12 b. Furthermore,part of each convex tooth pin 13 b protrudes from the axial end face ofthe output shaft body 13 a. That is, the output shaft 13 functions as agear having convex teeth of which the number of teeth is Z4.

In addition, in the above description, the convex tooth pins 13 b of theoutput shaft 13 are separately formed from the output shaft body 13 a,and are supported by the output shaft body 13 a. Other than this, ascorresponding to FIG. 1( b) and FIG. 2( b), the convex tooth pins 13 bmay be integrally formed with the output shaft body 13 a. In this case,the integrally formed convex tooth pins 13 b, as well as the portions ofthe convex tooth pins 13 b protruding from the axial end face of theoutput shaft body 13 a in the separately formed case, protrude from theaxially end face of a portion corresponding to the output shaft body 13a.

The outer ring 14 is formed in a cylindrical shape, and has a racewaysurface on its inner peripheral surface. The outer ring 14 ispress-fitted to the inclined surface 11 a of the input shaft 11. Thatis, the outer ring 14 is integrated with the input shaft 11, and isrotatable about the rotation central axis B.

The inner ring 15 (that corresponds to the “concave-convex gear” of theinvention) is formed in a substantially cylindrical shape. A rollingsurface 15 a is formed on the outer peripheral surface of the inner ring15. Furthermore, a plurality (G2) of nutation concave teeth 15 b areformed on one axial (right side in FIG. 1( a)) end face of the innerring 15 at equal intervals in the circumferential direction. Inaddition, a plurality (G3) of nutation concave teeth 15 c are formed onthe other axial (left side in FIG. 1( a)) end face of the inner ring 15at equal intervals in the circumferential direction.

The inner ring 15 is arranged on a radially inner side of the outer ring14, and holds the plurality of rolling elements (balls) 16. That is, theinner ring 15 has the rotation central axis B that is inclined withrespect to the rotation central axis A. Thus, the inner ring 15 isrotatable about the rotation central axis B with respect to the inputshaft 11. Furthermore, the inner ring 15 is rotatable about the rotationcentral axis A as the input shaft 11 rotates about the rotation centralaxis A through driving of the motor.

Furthermore, the inner ring 15 is arranged between the fixed shaft 12and the output shaft 13 in the axial direction. Specifically, the innerring 15 is arranged between the axial end face of the fixed shaft body12 a, supporting the convex tooth pins 12 b, and the axial end face ofthe output shaft body 13 a, supporting the convex tooth pins 13 b. Then,the one-side nutation concave teeth 15 b of the inner ring 15 mesh withthe convex tooth pins 12 b of the fixed shaft 12. In addition, theother-side nutation concave teeth 15 c of the inner ring 15 mesh withthe convex tooth pins 13 b of the output shaft 13.

Then, because the inner ring 15 wobbles about the rotation central axisA with respect to the fixed shaft 12, part (upper part in FIG. 1( a)) ofthe one-side nutation concave teeth 15 b of the inner ring 15 are inmesh with the convex tooth pins 12 b of the fixed shaft 12; however, theother part (lower part in FIG. 1( a)) of the one-side nutation concaveteeth 15 b are spaced apart from the convex tooth pins 12 b of the fixedshaft 12. In addition, because the inner ring 15 wobbles about therotation central axis A with respect to the output shaft 13, part (lowerpart in FIG. 1( a)) of the other-side nutation concave teeth 15 c of theinner ring 15 are in mesh with the convex tooth pins 13 b of the outputshaft 13; however, the other part (upper part in FIG. 1( a)) of theother-side nutation concave teeth 15 c are spaced apart from the convextooth pins 13 b of the output shaft 13.

Then, for example, the number of teeth Z1 of the convex tooth pins 12 bof the fixed shaft 12 is set so as to be smaller than the number ofteeth Z2 of the one-side nutation concave teeth 15 b of the inner ring15, and the number of teeth Z4 of the convex tooth pins 13 b of theoutput shaft 13 is set so as to be equal to the number of teeth Z3 ofthe other-side nutation concave teeth 15 c of the inner ring 15. By sodoing, the output shaft 13 reduces speed (performs differentialrotation) with respect to the rotation of the input shaft 11. That is,in this example, differential rotation is performed between the innerring 15 and the fixed shaft 12; whereas differential rotation is notperformed between the inner ring 15 and the output shaft 13. However,differential rotation may be caused to occur between the output shaft 13and the inner ring 15 such that the number of teeth Z4 of the convextooth pins 13 b of the output shaft 13 is set so as to be different fromthe number of teeth Z3 of the other-side nutation concave teeth 15 c ofthe inner ring 15. These may be set on the basis of a reduction gearratio where appropriate.

In the nutation gear set shown in FIG. 1( a), the meshing portionbetween the convex tooth pins 12 b of the fixed shaft 12 and theone-side nutation concave teeth 15 b of the inner ring 15, between whichdifferential rotation occurs, is as shown in FIG. 2( a). In addition, inthe nutation gear set shown in FIG. 1( b), the meshing portion betweenthe convex tooth pins 12 b of the fixed shaft 12 and the one-sidenutation concave teeth 15 b of the inner ring 15, between whichdifferential rotation occurs, is as shown in FIG. 2( b). Here, FIG. 2(a) shows a case where the convex tooth pins 12 b in the fixed shaft 12are separately formed from the fixed shaft body 12 a. FIG. 2( b) shows acase where the convex tooth pins 12 b in the fixed shaft 12 areintegrally formed with the fixed shaft body 12 a. The present embodimentmay be applied to any cases of FIG. 2( a) and FIG. 2( b). Note that,when differential rotation occurs between the output shaft 13 and theinner ring 15, the meshing portion between the convex tooth pins 13 b ofthe output shaft 13 and the other-side nutation concave teeth 15 c ofthe inner ring 15 is also similar to that of FIG. 2( a) or FIG. 2( b).Then, in the following description, only the meshing portion between thefixed shaft 12 and the nutation gear 15 will be described.

Here, each of the nutation concave teeth 15 b has a shape shown in FIG.3 and FIG. 4. That is, the sectional shape in the direction orthogonalto the tooth groove direction of each of the nutation concave teeth 15 bhas substantially a semicircular arc concave shape as a whole as shownin FIG. 2( a) and FIG. 4( a). More specifically, the sectional shape hasa shape such that circular arc concave-shaped opening edge portions aresagged. Furthermore, as shown in FIG. 3 and FIG. 4( b), each of thenutation concave teeth 15 b has a shape such that the groove widthwidens toward both ends in the tooth groove direction. This is becausethe number of teeth Z1 of the convex tooth pins 12 b is different fromthe number of teeth Z2 of the nutation concave teeth 15 b.

(2) Machining Method and Machining Device for Nutation Gear

(2.1) Basic Concept of Machining Method for Nutation Gear

Next, a machining method for the nutation concave teeth 15 b of theinner ring 15 (hereinafter, referred to as “nutation gear”) in the abovedescribed nutation gear set will be described. Note that a similarmachining method is employed for the nutation concave teeth 15 c of thenutation gear 15. First, the procedure of the machining method will bedescribed with reference to FIG. 5. As shown in FIG. 5,three-dimensional CAD models or mathematical models of the nutation gear15 and each convex tooth pin 12 b are generated (S1). This model is amovement model in which the nutation gear 15 and the fixed shaft 12perform differential rotation.

Subsequently, the relative movement trajectory of each convex tooth pin12 b with respect to a corresponding one of the nutation concave teeth15 b at the time when both perform differential rotation is extracted(S2) (that corresponds to “trajectory extracting step” and “trajectoryextracting means” of the invention). At the time of extracting therelative movement trajectory, it is presumed that the nutation concaveteeth 15 b are fixed and the convex tooth pins 12 b move with respect tothe nutation concave teeth 15 b, and the movement trajectory of eachconvex tooth pin 12 b is extracted. Then, the movement trajectory ofeach convex tooth pin 12 b includes the movement trajectory of thecentral axis 12X (hereinafter, referred to as “reference axis”) of theconvex tooth pin 12 b and the movement trajectory of the central point(hereinafter, referred to as “pin central point”) of the convex toothpin 12 b in the central axis direction. Note that the reference axis 12Xof the convex tooth pin 12 b corresponds to an axis parallel to the lineof intersection of the tooth thickness central plane and referenceconical surface of the convex tooth pin 12 b.

Subsequently, the extracted relative movement trajectory of each convextooth pin 12 b with respect to the nutation gear 15 is subjected tocoordinate conversion to generate an NC program that is the movementtrajectory of a working tool (S3) (that corresponds to “coordinateconversion step” and “coordinate conversion means” of the invention).The NC program corresponds to the movement trajectory of the workingtool for machining the nutation concave teeth 15 b in a workpiececoordinate system. This will be described in detail later.

Subsequently, at least one of a disc-shaped workpiece and the workingtool is moved on the basis of the generated NC program (S4) (thatcorresponds to “machining step” and “machining means” of the invention).That is, at least one of the disc-shaped workpiece and the working toolis moved such that the relative movement trajectory of the working toolwith respect to the disc-shaped workpiece coincides with the movementtrajectory of each convex tooth pin 12 b, extracted in step S2. Here,the disc-shaped workpiece is a material that is formed into the shape ofthe nutation gear 15 and that have not been machined for the nutationconcave teeth 15 b yet.

Hereinafter, the trajectory extracting step, the coordinate conversionstep and the machining step will be described in detail.

(2.2) Trajectory Extracting Step (Trajectory Extracting Means)

The trajectory extracting step will be described with reference to FIG.6( a 1), FIG. 6( a 2), FIG. 6( b 1), FIG. 6( b 2), FIG. 6( c 1) and FIG.6( c 2). For the shape of each convex tooth pin 12 b, only the portionof each convex tooth pin 12 b, protruding from the fixed shaft body 12 aof the fixed shaft 12 shown in FIG. 2( a) and FIG. 2( b), is shown. Thatis, in the drawings of FIG. 6( a 1) to FIG. 6( c 2), the convex toothpin 12 b shows the portion common to the convex tooth pins 12 b shown inFIG. 2( a) and FIG. 2( b).

In a state before the convex tooth pin 12 b meshes with the nutationconcave tooth 15 b, as shown in FIG. 6( a 1), when viewed in therotation central axis direction (“B” in FIG. 1( a) and FIG. 1( b)) ofthe nutation gear 15, the reference axis 12X of the convex tooth pin 12b is inclined rightward in FIG. 6( a 1) with respect to the tooth groovedirection 15X of the nutation concave tooth 15 b. Furthermore, as shownin FIG. 6( a 2), when viewed in the direction orthogonal to the toothgroove direction 15X along the contact surface of the reference conicalsurface of the nutation concave tooth 15 b, the reference axis 12X ofthe convex tooth pin 12 b is inclined leftward in FIG. 6( a 2) withrespect to the tooth groove direction 15X of the nutation concave teeth15 b. Then, in both drawings, the pin central point 12C of the convextooth pin 12 b is located at a position that deviates from the toothgroove direction 15X of the nutation concave tooth 15 b.

Subsequently, in a state where the convex tooth pin 12 b is in mesh withthe nutation concave tooth 15 b, as shown in FIG. 6( b 1) and FIG. 6( b2), the tooth groove direction 15X of the nutation concave tooth 15 bcoincides with the reference axis 12X of the convex tooth pin 12 b. Ofcourse, the pin central point 12C of the convex tooth pin 12 b alsocoincides with the tooth groove direction 15X of the nutation concavetooth 15 b.

Subsequently, in a state where the convex tooth pin 12 b is separatedfrom a meshed state with the nutation concave tooth 15 b, as shown inFIG. 6( c 1), when viewed in the rotation central axis direction (“B” inFIG. 1( a) and FIG. 1( b)) of the nutation gear 15, the reference axis12X of the convex tooth pin 12 b is inclined leftward in FIG. 6( c 1)with respect to the tooth groove direction 15X of the nutation concavetooth 15 b. Furthermore, as shown in FIG. 6( c 2), when viewed in thedirection orthogonal to the tooth groove direction 15X along the contactsurface of the reference conical surface of the nutation concave tooth15 b, the reference axis 12X of the convex tooth pin 12 b is inclinedleftward in FIG. 6( c 2) with respect to the tooth groove direction 15Xof the nutation concave tooth 15 b. Then, in both drawings, the pincentral point 12C of the convex tooth pin 12 b is located at a positionthat deviates from the tooth groove direction 15X of the nutationconcave tooth 15 b.

That is, the movement trajectory of the reference axis 12X of the convextooth pin 12 b and the movement trajectory of the pin central point 12Care as shown in FIG. 7.(a) and FIG. 7( b). The movement trajectory ofthe reference axis 12X may be decomposed into and expressed by a firstlinear axis, a second linear axis, the third linear axis, the fourthrotation axis, a fifth rotation axis and the sixth indexing axis. Here,in FIG. 7 and the following drawings, numeric characters in circlescoincide with the respective axis numbers. For example, the axisindicated such that the numeric character in circle is “1” is the firstlinear axis.

That is, the first linear axis is an axis along which the referenceposition (predetermined position) of the convex tooth pin 12 b is movedin the direction orthogonal to a plane that is tangent to a concavetooth forming face (“axial end face” in the present embodiment) of thedisc-shaped workpiece (nutation gear 15). The second linear axis is anaxis along which the reference position of the convex tooth pin 12 b ismoved in the tooth groove direction of the nutation concave tooth 15 bin the plane that is tangent to the concave tooth forming face of thedisc-shaped workpiece (nutation gear 15). The third linear axis is anaxis along which the reference position of the convex tooth pin 12 b ismoved in the direction orthogonal to the second linear axis in the planethat is tangent to the concave tooth forming face of the disc-shapedworkpiece (nutation gear 15).

The fourth rotation axis is an axis along which the reference positionof the convex tooth pin 12 b is rotated about the first linear axis. Thefifth rotation axis is an axis along which the reference position of theconvex tooth pin 12 b is rotated about the third linear axis. The fourthrotation axis and the fifth rotation axis shown here are axes thatrotate about the pin central point 12C of the convex tooth pin 12 b. Thesixth indexing axis is an axis that coincides with the rotation centralaxis B (shown in FIG. 1( a) and FIG. 1( b)) of the nutation gear 15 andthat indexes the rotation phase of the nutation gear 15.

(2.3) Coordinate Conversion Step (Coordinate Conversion Means)

Here, the subject machine tool in the present embodiment has a machineconfiguration having first to sixth axes. That is, the NC program in thepresent embodiment is expressed by the three linear axes and the threerotation axes as in the case of the above described movement trajectoryof each convex tooth pin 12 b. That is, in the coordinate conversionstep, the NC program that includes the three linear axes and the threerotation axes is generated so as to perform movement substantiallysimilar to the movement trajectory of each convex tooth pin 12 b.

(2.4) Machining Step (Machining Means)

The working tool in the present embodiment may be any tool as long as itis possible to express the outer peripheral shape of the convex toothpin 12 b. A first working tool is a tool having a circular columnar pinshape that is coincident with or small similar to the outer peripheralshape of the convex tooth pin 12 b and that rotates about the pincentral axis. In addition, a second working tool is a toroidal grindingwheel 30 as shown in FIG. 8( a) and FIG. 8( b). The toroidal grindingwheel 30 is a disc-shaped tool shown in FIG. 8( a), and its outerperipheral edge shape is, for example, a circular arc convex shape shownin FIG. 8( b). The width of the toroidal grinding wheel 30, shown inFIG. 8( b), is smaller than or equal to the diameter of the convex toothpin 12 b. Through infeed operation at multiple portions at which thecentral axis of the toroidal grinding wheel 30 is shifted in the toothgroove direction of the concave tooth 15 b, the convex tooth pin 12 b isspuriously expressed by the toroidal grinding wheel 30. In addition, acirculating belt-shaped tool shown in FIG. 9( a) and FIG. 9( b) may alsobe used. As shown in FIG. 9( a), the belt-shaped tool has a straightportion in the circulating direction. Then, the outer peripheral shapeof the straight portion is coincident with or similar to part of theouter peripheral shape of the convex tooth pin 12 b.

Then, in the machining step, machining is performed on the basis of theNC program subjected to coordinate conversion in the coordinateconversion step. That is, as shown in FIG. 10, the disc-shaped workpieceand the working tool are relatively moved by the six axes formed of thefirst linear axis, the second linear axis, the third linear axis, thefourth rotation axis (about the pin central point 12C), the fifthrotation axis (about the pin central point 12C) and the sixth indexingaxis (about the rotation central axis B of the nutation gear 15) tomachine the nutation concave tooth 15 b. That is, when the working toolis a pin-shaped working tool, the pin-shaped working tool is moved so asto perform movement similar to that of the convex tooth pin 12 b. Inaddition, in the case of the circulating belt-shaped tool, the straightportion of the tool is caused to perform movement similar to that of thepin-shaped working tool. Note that movement in the case of the toroidalgrinding wheel 30 will be described in detail in other embodimentsdescribed later.

(3) Advantageous Effects of First Embodiment

According to the present embodiment, a six-axis NC machine tool is usedto make it possible to machine the nutation concave teeth 15 b of thenutation gear 15. That is, even when the outside diameter of thenutation gear 15 varies or the shape of each nutation concave tooth 15 bvaries, the nutation concave teeth 15 b may be machined by the same NCmachine tool.

In addition, the nutation gear 15 is a concave-convex gear that rotatesabout an intersecting axis with respect to a mating gear (the fixedshaft 12 or the output shaft 13). Because of such a configuration, themeshing rate of both gears increases. Therefore, it is possible toreduce size, increase strength and achieve quietness. On the other hand,in order to achieve desirable tooth contact, it is required to form atooth flank shape having an extremely high accuracy, so there is aproblem that machining of a tooth flank shape is not easy. In contrastto this, by applying the machining method according to the presentembodiment, the nutation concave teeth 15 b and 15 c of the nutationgear 15 with an intersecting axis may be easily and highly accuratelyformed. As a result, it is possible to reduce machining cost in the caseof accuracy equivalent to the existing art.

Here, because the number of teeth Z1 of the convex tooth pins 12 b isdifferent from the number of teeth Z2 of the nutation concave teeth 15b, the fixed shaft 12 and the nutation gear 15 are configured to be ableto reliably perform differential rotation. Then, because the number ofteeth is different therebetween, the shape of each of the nutationconcave teeth 15 b is an extremely complex shape as shown in FIG. 2 toFIG. 4.

Furthermore, the sectional shape of the convex tooth pin 12 b in thedirection orthogonal to the reference axis is a circular arc shape. Byso doing, the fixed shaft 12 and the nutation gear 15 are able toextremely smoothly perform differential rotation. On the other hand,machining of the nutation concave teeth 15 b of the nutation gear 15becomes complicated. Because the sectional shape of the convex tooth pin12 b in the direction orthogonal to the reference axis is a circular arcshape, each of the nutation concave teeth 15 b has a sectional shapeapproximate to a circular arc concave shape as a whole, and,specifically, has a sectional shape of which the opening edge portionsof the circular arc concave shape are sagged. In this way, even wheneach of the nutation concave teeth 15 b has a complex shape, accordingto the present embodiment, it is possible to reliably and highlyaccurately perform machining. As a result, it is possible to form thenutation gear 15 having high performance at low cost.

In addition, relative movement between the nutation gear 15 and thefixed shaft 12 is three-dimensionally complex movement; however, thereference axis 12X of the convex tooth pin 12 b is used to thereby makeit possible to reliably understand the relative movement trajectory ofthe convex tooth pin 12 b.

In addition, when the working tool has a shape that is coincident withor similar to the convex tooth pin 12 b, movement of the working tool isset so as to be substantially similar to that of the convex tooth pin 12b to thereby make it possible to form the optimal nutation concave teeth15 b. This also applies to the case where the circulating belt-shapedtool is used as the working tool.

In addition, the relative movement trajectory of the convex tooth pin 12b is converted to movement of the working tool in the workpiececoordinate system. In the present embodiment, the movement of the convextooth pin 12 b is caused to substantially coincide with the movement ofthe pin-shaped working tool. Thus, the movement trajectory of the convextooth pin 12 b, extracted in the trajectory extracting step, and the NCprogram are not substantially significantly different from each other.However, depending on the type of working tool, the relative movementtrajectory extracted in the trajectory extracting step and the movementtrajectory of the working tool in the workpiece coordinate system maydiffer from each other. That is, by providing the coordinate conversionstep, the NC program based on the type of working tool may be generated.This point is particularly effective in other embodiments.

Second Embodiment Five-Axis Configuration (Three Linear Axes and TwoRotation Axes) (First Example of Omission of Fourth Rotation Axis)

A machining method and machining device for a nutation gear of anutation gear set according to a second embodiment will be describedwith reference to FIG. 11. The machining device in the presentembodiment shows the case of a five-axis configuration having threeorthogonal linear axes and two rotation axes. The fourth rotation axisin the first embodiment is omitted. Specifically, movement along thefourth rotation axis described in the first embodiment is decomposedinto movement along the sixth indexing axis and movement along the thirdlinear axis.

Here, in the present embodiment, “model generation” (S1) and “trajectoryextracting step” (S2) in the first embodiment are the same. That is, themovement trajectory of the convex tooth pin 12 b, extracted in thetrajectory extracting step, is expressed by the three linear axes andthe three rotation axes.

Subsequently, in the coordinate conversion step, first, the process ofdecomposing movement along the fourth rotation axis into movement alongthe sixth indexing axis and movement along the third linear axis to omitmovement along the fourth rotation axis is executed. Here, the fourthrotation axis is an axis that rotates about an axis parallel to thesixth indexing axis. Then, as shown in FIG. 11, the center of the fourthrotation axis, that is, the pin central point 12C of the convex toothpin 12 b, is brought into coincidence with the rotation center of thesixth indexing axis (the rotation central axis B of the nutation gear15). At this time, at the time of shifting the pin central point 12C ofthe convex tooth pin 12 b, the pin central point 12C is shifted alongthe reference axis 12X of the convex tooth pin 12 b. That is, it ispresumed that the tooth length of the convex tooth pin 12 b is infinite,and the rotation center of the shifted fourth rotation axis moves alongthe third linear axis. In this way, when the fourth rotation axis isdecomposed into the sixth indexing axis and the third linear axis,movement along the fourth rotation axis may be omitted. As a result, therelative movement trajectory of the convex tooth pin 12 b is expressedby three linear axes and two rotation axes.

Furthermore, subsequently, in the coordinate conversion step, an NCprogram expressed by the three linear axes and the two rotation axes isgenerated on the basis of the calculated movement trajectories of thethree linear axes, that is, the first linear axis, the second linearaxis and the third linear axis, and the two rotation axes, that is, thefifth rotation axis and the sixth indexing axis. Note that, the subjectmachine tool in the present embodiment has a machine configurationhaving first to third, fifth and sixth axes.

Subsequently, in the machining step, as in the case of the firstembodiment, a tool having a pin shape that coincides with the outerperipheral shape of the convex tooth pin 12 b is assumed as the workingtool. Then, in the machining step, machining is performed on the basisof the five-axis configuration NC program subjected to coordinateconversion in the coordinate conversion step. That is, as shown in FIG.11, the disc-shaped workpiece and the working tool are relatively movedby the five axes formed of the first linear axis, the second linearaxis, the third linear axis, the fifth rotation axis (about the pincentral point 12C) and the sixth indexing axis (about the rotationcentral axis B of the nutation gear 15) to machine the nutation concavetooth 15 b.

In this way, according to the present embodiment, movement along thefourth rotation axis is omitted to make it possible to allow machiningwith five axes. Thus, the number of component axes of a machine toolthat is able to machine the nutation concave teeth 15 b may be reduced,so it is possible to reduce the cost of the machine tool.

Third Embodiment Five-Axis Configuration (Three Linear Axes and TwoRotation Axes) (Second Example of Omission of Fourth Rotation Axis)

A machining method and machining device for a nutation gear of anutation gear set according to a third embodiment will be described withreference to FIG. 12. The machining device in the present embodimentshows the case of a five-axis configuration having three orthogonallinear axes and two rotation axes. The fourth rotation axis in the firstembodiment is omitted. Specifically, movement along the fourth rotationaxis described in the first embodiment is decomposed into movement alongthe sixth indexing axis and movement along the second linear axis.

Here, in the present embodiment, “three-dimensional CAD modelgeneration” (S1) and “trajectory extracting step” (S2) in the firstembodiment are the same. That is, the movement trajectory of the convextooth pin 12 b, extracted in the trajectory extracting step, isexpressed by the three linear axes and the three rotation axes.

Subsequently, in the coordinate conversion step, first, the process ofdecomposing movement along the fourth rotation axis into movement alongthe sixth indexing axis and movement along the second linear axis toomit movement along the fourth rotation axis is executed. Here, as isdescribed in the second embodiment, the fourth rotation axis is an axisthat rotates about an axis parallel to the sixth indexing axis. Then, asshown in FIG. 12, the center of the fourth rotation axis, that is, thepin central point 12C of the convex tooth pin 12 b, is brought intocoincidence with the rotation center of the sixth indexing axis (therotation central axis B of the nutation gear 15). At this time, at thetime of shifting the pin central point 12C of the convex tooth pin 12 b,the pin central point 12C is shifted along the reference axis 12X of theconvex tooth pin 12 b. That is, the rotation center of the shiftedfourth rotation axis moves along the second linear axis. In this way,the fourth rotation axis is decomposed into the sixth indexing axis andthe second linear axis to thereby make it possible to omit the movementof the fourth rotation axis. As a result, the relative movementtrajectory of the convex tooth pin 12 b is expressed by three linearaxes and two rotation axes.

Furthermore, subsequently, in the coordinate conversion step, an NCprogram expressed by the three linear axes and the two rotation axes isgenerated on the basis of the calculated movement trajectories of thethree linear axes, that is, the first linear axis, the second linearaxis and the third linear axis, and the two rotation axes, that is, thefifth rotation axis and the sixth indexing axis. Note that, the subjectmachine tool in the present embodiment has a machine configurationhaving first to third, fifth and sixth axes.

Subsequently, in the machining step, as in the case of the firstembodiment, a tool having a pin shape that coincides with the outerperipheral shape of the convex tooth pin 12 b is assumed as the workingtool. Then, in the machining step, machining is performed on the basisof the five-axis configuration NC program subjected to coordinateconversion in the coordinate conversion step. That is, as shown in FIG.12, the disc-shaped workpiece and the working tool are relatively movedby the five axes formed of the first linear axis, the second linearaxis, the third linear axis, the fifth rotation axis (about the pincentral point 12C) and the sixth indexing axis (about the rotationcentral axis B of the nutation gear 15) to machine the nutation concavetooth 15 b.

In this way, according to the present embodiment, movement along thefourth rotation axis is omitted to make it possible to allow machiningwith five axes. Thus, the number of component axes of a machine toolthat is able to machine the nutation concave teeth 15 b may be reduced,so it is possible to reduce the cost of the machine tool.

Fourth Embodiment Four-Axis Configuration (Two Linear Axes and TwoRotation Axes) (Omission of Second Linear Axis and Fourth Rotation Axis)

A machining method and machining device for a nutation gear of anutation gear set according to a fourth embodiment will be describedwith reference to FIG. 11, and FIG. 13 to FIG. 15. The machining devicein the present embodiment shows the case of a four-axis configurationhaving two orthogonal linear axes and two rotation axes. The fourthrotation axis and the second linear axis in the first embodiment areomitted. Specifically, movement along the fourth rotation axis describedin the first embodiment is decomposed into movement along the sixthindexing axis and movement along the third linear axis, and the secondlinear axis is decomposed into the first linear axis and the thirdlinear axis.

Here, in the present embodiment, “model generation” (S1) and “trajectoryextracting step” (S2) in the first embodiment are the same. That is, themovement trajectory of the convex tooth pin 12 b, extracted in thetrajectory extracting step, is expressed by the three linear axes andthe three rotation axes.

Subsequently, in the coordinate conversion step, first, as described inthe second embodiment, as shown in FIG. 11, in the trajectory extractingstep, the process of decomposing movement along the fourth rotation axisinto movement along the sixth indexing axis and movement along the thirdlinear axis to omit movement along the fourth rotation axis is executed.That is, at this time point, the relative movement trajectory of theconvex tooth pin 12 b is expressed by the three linear axes and the tworotation axes.

Furthermore, in the present embodiment, in the coordinate conversionstep, the process of omitting movement along the second linear axis isexecuted. The outline of this process will be described with referenceto FIG. 13( a) and FIG. 13( b). As shown in FIG. 13( a) and FIG. 13( b),it is presumed that the tooth length of the convex tooth pin 12 b isinfinite, and the pin central point 12C of the convex tooth pin 12 b isshifted along the reference axis 12X of the convex tooth pin 12 b.Furthermore, the pin central point 12C of the convex tooth pin 12 b isshifted into the plane that passes through the first linear axis and thethird linear axis. The details of this point are shown in FIG. 14( a)and FIG. 14( b). The pin central points 12C each are shifted into theplane that passes through the first linear axis and the third linearaxis. In this way, when movement along the second linear axis isdecomposed into movement along the first linear axis and movement alongthe third linear axis, movement along the second linear axis may beomitted.

Note that, in the above description, for the sake of easy description, aprocessing method in which the fourth rotation axis is omitted first andthen the second linear axis is omitted is described; instead, theprocesses of omitting the axes may be reversed, and the same result maybe obtained. In addition, as for the process, the process of omittingthe fourth rotation axis and the process of omitting the second linearaxis may be executed simultaneously.

Thus, in the present embodiment, the second linear axis and the fourthrotation axis are omitted with respect to the first embodiment from therelative movement trajectory of the convex tooth pin 12 b. That is, asshown in FIG. 15( a) and FIG. 15( b), the finally obtained relativemovement trajectory of the convex tooth pin 12 b is expressed by the twolinear axes, that is, the first linear axis and the third linear axis,and the two rotation axes, that is, the fifth rotation axis and thesixth indexing axis.

Furthermore, subsequently, in the coordinate conversion step, an NCprogram expressed by the two linear axes and the two rotation axes isgenerated on the basis of the calculated movement trajectories of thetwo linear axes, that is, the first linear axis and the third linearaxis, and the two rotation axes, that is, the fifth rotation axis andthe sixth indexing axis. Note that, the subject machine tool in thepresent embodiment has a machine configuration having first, third,fifth and sixth axes.

Subsequently, in the machining step, as in the case of the firstembodiment, a tool having a pin shape that coincides with the outerperipheral shape of the convex tooth pin 12 b is assumed as the workingtool. Then, in the machining step, machining is performed on the basisof the four-axis configuration NC program subjected to coordinateconversion in the coordinate conversion step. That is, as shown in FIG.15, the disc-shaped workpiece and the working tool are relatively movedby the four axes formed of the first linear axis, the third linear axis,the fifth rotation axis (about the pin central point 12C) and the sixthindexing axis (about the rotation central axis B of the nutation gear15) to machine the nutation concave tooth 15 b.

In this way, according to the present embodiment, movement along thefourth rotation axis and movement along the second linear axis areomitted to make it possible to allow machining with four axes. Thus, thenumber of component axes of a machine tool that is able to machine thenutation concave teeth 15 b may be reduced, so it is possible to reducethe cost of the machine tool.

Fifth Embodiment Four-Axis Configuration (Two Linear Axes and TwoRotation Axes) (Omission of Third Linear Axis and Fourth Rotation Axis)

A machining method and machining device for a nutation gear of anutation gear set according to a fifth embodiment will be described withreference to FIG. 12, and FIG. 16 to FIG. 18. The machining device inthe present embodiment shows the case of a four-axis configurationhaving two orthogonal linear axes and two rotation axes. The fourthrotation axis and the third linear axis in the first embodiment areomitted. Specifically, movement along the fourth rotation axis describedin the first embodiment is decomposed into movement along the sixthindexing axis and movement along the second linear axis, and the thirdlinear axis is decomposed into the first linear axis and the secondlinear axis.

Here, in the present embodiment, “model generation” (S1) and “trajectoryextracting step” (S2) in the first embodiment are the same. That is, themovement trajectory of the convex tooth pin 12 b, extracted in thetrajectory extracting step, is expressed by the three linear axes andthe three rotation axes.

Subsequently, in the coordinate conversion step, first, as described inthe third embodiment, as shown in FIG. 12, in the trajectory extractingstep, the process of decomposing movement along the fourth rotation axisinto movement along the sixth indexing axis and movement along thesecond linear axis to omit movement along the fourth rotation axis isexecuted. That is, at this time point, the relative movement trajectoryof the convex tooth pin 12 b is expressed by the three linear axes andthe two rotation axes.

Furthermore, in the present embodiment, in the coordinate conversionstep, the process of omitting movement along the third linear axis isexecuted. The outline of this process will be described with referenceto FIG. 16( a) and FIG. 16( b). As shown in FIG. 16( a) and FIG. 16( b),it is presumed that the tooth length of the convex tooth pin 12 b isinfinite, and the pin central point 12C of the convex tooth pin 12 b isshifted along the reference axis 12X of the convex tooth pin 12 b.Furthermore, the pin central point 12C of the convex tooth pin 12 b isshifted into the plane that passes through the first linear axis and thesecond linear axis. The details of this point are shown in FIG. 17( a)and FIG. 17( b). The pin central points 12C each are shifted into theplane that passes through the first linear axis and the second linearaxis. In this way, when movement along the third linear axis isdecomposed into movement along the first linear axis and movement alongthe second linear axis, movement along the third linear axis may beomitted.

Note that, in the above description, for the sake of easy description, aprocessing method in which the fourth rotation axis is omitted first andthen the third linear axis is omitted is described; instead, theprocesses of omitting the axes may be reversed, and the same result maybe obtained. In addition, as for the process, the process of omittingthe fourth rotation axis and the process of omitting the third linearaxis may be executed simultaneously.

Thus, in the present embodiment, the fourth rotation axis and the thirdlinear axis are omitted with respect to the first embodiment from therelative movement trajectory of the convex tooth pin 12 b. That is, asshown in FIG. 18( a) and FIG. 18( b), the finally obtained relativemovement trajectory of the convex tooth pin 12 b is expressed by the twolinear axes, that is, the first linear axis and the second linear axis,and the two rotation axes, that is, the fifth rotation axis and thesixth indexing axis.

Furthermore, subsequently, in the coordinate conversion step, an NCprogram expressed by the two linear axes and the two rotation axes isgenerated on the basis of the calculated movement trajectories of thetwo linear axes, that is, the first linear axis and the second linearaxis, and the two rotation axes, that is, the fifth rotation axis andthe sixth indexing axis. Note that, the subject machine tool in thepresent embodiment has a machine configuration having first, second,fifth and sixth axes.

Subsequently, in the machining step, as in the case of the firstembodiment, a tool having a pin shape that coincides with the outerperipheral shape of the convex tooth pin 12 b is assumed as the workingtool. Then, in the machining step, machining is performed on the basisof the four-axis configuration NC program subjected to coordinateconversion in the coordinate conversion step. That is, as shown in FIG.18, the disc-shaped workpiece and the working tool are relatively movedby the four axes formed of the first linear axis, the second linearaxis, the fifth rotation axis (about the pin central point 12C) and thesixth indexing axis (about the rotation central axis B of the nutationgear 15) to machine the nutation concave tooth 15 b.

In this way, according to the present embodiment, movement along thefourth rotation axis and movement along the second linear axis areomitted to make it possible to allow machining with four axes. Thus, thenumber of component axes of a machine tool that is able to machine thenutation concave teeth 15 b may be reduced, so it is possible to reducethe cost of the machine tool.

Sixth Embodiment Four-Axis Configuration (Three Linear Axes and OneRotation Axis) and Toroidal Grinding Wheel

A machining method and machining device for a nutation gear of anutation gear set according to a sixth embodiment will be described withreference to FIG. 8, FIG. 11, FIG. 12, and FIG. 19 to FIG. 22. Themachining device in the present embodiment shows the case of a four-axisconfiguration having three orthogonal linear axes and one rotation axis.The fourth rotation axis and the fifth rotation axis in the firstembodiment are omitted. Specifically, movement along the fourth rotationaxis described in the first embodiment is decomposed into movement alongthe sixth indexing axis and movement along the second linear axis, andthe fifth rotation axis is decomposed into the first linear axis and thesecond linear axis. In addition to this, a toroidal grinding wheel(disc-shaped tool) is used as the working tool.

(4) Machining Method and Machining Device for Nutation Gear

(4.1) Basic Concept of Machining Method for Nutation Gear

The basic concept of the machining method for the nutation concave teeth15 b of the nutation gear 15 in the nutation gear set will be described.In the machining method in the present embodiment, the toroidal grindingwheel 30 shown in FIG. 8 is used. The toroidal grinding wheel 30 is adisc-shaped tool shown in FIG. 8( a), and its outer peripheral edgeshape is a circular arc convex shape shown in FIG. 8( b).

When the toroidal grinding wheel 30 is used to machine the nutationconcave teeth 15 b, movement shown in FIG. 19 is allowed. That is, thefifth rotation axis in the first embodiment may be expressed by thefirst linear axis and the second linear axis owing to the toroidalgrinding wheel 30. However, when a series of movements (movementcorresponding to the movement trajectory of the convex tooth pin 12 b)of the toroidal grinding wheel 30 with respect to the nutation concavetooth 15 b is performed once, as shown in FIG. 20( a) and FIG. 20( b), acutting remainder occurs at the nutation concave tooth 15 b.

Then, as shown in FIG. 21, through infeed operation at multiple portionsat which the central axis of the toroidal grinding wheel 30 is shiftedin the tooth groove direction of the nutation concave tooth 15 b, theconvex tooth pin 12 b is spuriously expressed by the toroidal grindingwheel 30. As a result, it is possible to reduce a cutting remainder ofthe nutation concave tooth 15 b. FIG. 21 shows an example in whichinfeed operation is performed at three positions. In this way, a seriesof movements of the toroidal grinding wheel 30 is performed at multipleinfeed operation positions to thereby make it possible to machine thenutation concave tooth 15 b with further high accuracy.

In consideration of this basic concept, the procedure of the machiningmethod according to the present embodiment will be descried withreference to FIG. 22. As shown in FIG. 22, three-dimensional CAD modelsof the nutation gear 15 and each convex tooth pin 12 b are generated(S11). This model is a movement model in which the nutation gear 15 andthe fixed shaft 12 perform differential rotation.

Subsequently, the relative movement trajectory of each convex tooth pin12 b with respect to a corresponding one of the nutation concave teeth15 b at the time when both perform differential rotation is extracted(S12) (that corresponds to “trajectory extracting step” and “trajectoryextracting means” of the invention). At the time of extracting therelative movement trajectories, first, the same process as the processin the trajectory extracting step is executed. That is, in thetrajectory extracting step, the relative movement trajectories of thereference axis 12X and pin central point 12C of the convex tooth pin 12b with respect to the nutation gear 15 are extracted. That is, at thistime point, the movement trajectory of the convex tooth pin 12 b,extracted in the trajectory extracting step, is expressed by the threelinear axes and the three rotation axes.

Subsequently, the extracted relative movement trajectory of the convextooth pin 12 b with respect to the nutation gear 15 is subjected tocoordinate conversion to generate an NC program that is the movementtrajectory of the toroidal grinding wheel 30 (S13) (that corresponds to“coordinate conversion step” and “coordinate conversion means” of theinvention).

First, in the coordinate conversion step, as described in the secondembodiment or the third embodiment, as shown in FIG. 11 or FIG. 12, theprocess of decomposing movement along the fourth rotation axis intomovement along the sixth indexing axis and movement along the thirdlinear axis (or the second linear axis) to omit movement along thefourth rotation axis is executed. That is, at this time point, therelative movement trajectory of the convex tooth pin 12 b is expressedby the three linear axes and the two rotation axes.

Furthermore, in the present embodiment, in the coordinate conversionstep, the process of omitting movement along the fifth rotation axis isexecuted. As described above, this process is achieved by using thetoroidal grinding wheel 30. That is, at this time point, the relativemovement trajectory of the convex tooth pin 12 b is expressed by thethree linear axes and the one rotation axis. Here, at this time point,the position of infeed operation of the toroidal grinding wheel 30 inthe tooth groove direction is set at one portion. Furthermore,subsequently, the calculated relative movement trajectory of the convextooth pin 12 b with respect to the nutation gear 15 is subjected tocoordinate conversion to generate an NC program that is the movementtrajectory of the working tool.

Subsequently, the toroidal grinding wheel 30 and the disc-shapedworkpiece (nutation gear 15) are relatively moved to perform machiningsimulation (S14) (that corresponds to “simulation step” and “simulationmeans” of the invention). That is, the toroidal grinding wheel 30 ismoved in accordance with the generated NC program with respect to thedisc-shaped workpiece before the nutation concave teeth 15 b aremachined to generate the shape of the machined disc-shaped workpiecethrough machining simulation.

Subsequently, a preset ideal shape model is compared with the shape ofthe result of machining simulation to calculate a deviation (S15).Subsequently, it is determined whether the calculated deviation issmaller than or equal to a preset allowable value (S16).

Then, when the calculated deviation exceeds the allowable value (N inS16), the position of infeed operation is calculated by shifting thecentral axis of the toroidal grinding wheel 30 in the tooth groovedirection of the nutation concave tooth 15 b (S17) (that corresponds to“cutting position calculation step” of the invention). Here, forexample, infeed operation is performed such that the central axis of thetoroidal grinding wheel 30 is shifted to two portions in the toothgroove direction of the nutation concave tooth 15 b. Here, in thecutting position calculation step, the position of infeed operation iscalculated so that a deviation between the shape of the result ofmachining simulation and the ideal shape model reduces and a machiningtime reduces.

When calculation of the position of infeed operation is completed, theprocess returns to step S13, and coordinate conversion process isexecuted again on the basis of the calculated position of infeedoperation. That is, through a repetition of step S13 to step S17, in thecutting position calculation step, the position of infeed operation iscalculated so that a deviation between the shape of the result ofmachining simulation and the ideal shape model is smaller than or equalto the set allowable value and a machining time is minimized.

Then, when the calculated deviation is smaller than or equal to theallowable value (Y in S16), at least one of the disc-shaped workpieceand the toroidal grinding wheel 30 is moved on the basis of thegenerated NC program (S18) (that corresponds to “machining step” and“machining means” of the invention).

In this way, according to the present embodiment, by using the toroidalgrinding wheel 30, movement along the fourth rotation axis and movementalong the fifth rotation axis are omitted to make it possible to allowmachining with four axes. Thus, the number of component axes of amachine tool that is able to machine the nutation concave teeth 15 b maybe reduced, so it is possible to reduce the cost of the machine tool.However, on the contrary, by using the toroidal grinding wheel 30, ageometrical deviation, that is, cutting remainder, occurs. Then,machining simulation is performed and then comparison is made with theideal shape model to thereby make it possible to reliably form thenutation concave teeth 15 b with high accuracy. Furthermore, a machiningcondition with a shortest period of time may be calculated.

Note that, as long as at least a four-axis configuration formed of thethree linear axes and the one rotation axis described in the presentembodiment is provided, the toroidal grinding wheel 30 is used to makeit possible to machine the nutation concave teeth 15 b of the nutationgear 15. That is, in the first embodiment (six-axis configuration) andthe second embodiment (five-axis configuration formed of the threelinear axes and the two rotation axes) as well, machining using thetoroidal grinding wheel 30 is allowed.

Seventh Embodiment

In the above first to sixth embodiments, the machining method in whichthe nutation gear of the nutation gear set is set as a machining targetis described. The nutation gear set is configured to include two sets ofthe relationship between the concave-convex gear and the mating gear ofwhich the respective rotation central axes intersect with each other. Atorque transmission device that is configured to include a set of theabove relationship between the concave-convex gear and the mating gearwill be described with reference to FIG. 23( a) and FIG. 23( b).

Here, FIG. 23( a) shows a case where convex tooth pins 112 b areseparately formed from an input shaft body 112 a, and FIG. 23( b) showsa case where the convex tooth pins 112 b are integrally formed with theinput shaft body 112 a.

As shown in FIG. 23( a) and FIG. 23( b), the torque transmission deviceis formed of an input shaft 112 and an output shaft 115. The input shaft112 (that corresponds to a “mating gear” of the invention) is formed ofsubstantially similar configuration to that of the output shaft 13 inthe first embodiment. The input shaft 112 is formed of the input shaftbody 112 a and the plurality of convex tooth pins 112 b. The input shaftbody 112 a (that corresponds to a “mating gear body” of the invention)is a cylindrical member having an axis A as a rotation central axis.Then, the input shaft body 112 a is supported by a housing (not shown)via a bearing so as to be rotatable about the rotation central axis A.

The output shaft 115 (that corresponds to a “concave-convex gear” of theinvention) has substantially the same shape of one of the end faces ofthe inner ring (nutation gear) 15 in the first embodiment. That is, aplurality (G2) of concave teeth 115 b are formed on an axially one (leftside in FIG. 23( a) and FIG. 23( b)) end face of the output shaft 115 atequal intervals in the circumferential direction. The output shaft 115is supported by the housing (not shown) via a bearing so as to berotatable about a rotation central axis B inclined with respect to therotation central axis A. Then, another torque transmission member iscoupled to the axially other side (right side in FIG. 23( a) and FIG.23( b)) of the output shaft 115.

In this way, when the concave teeth of the output shaft 115 that rotatesabout the rotation central axis B that intersects with the rotationcentral axis A of the input shaft 112 are set as a machining target, themachining method in the above described embodiments may be appliedsimilarly. Then, similar advantageous effects are obtained.

Others

In addition, the above embodiments are described on the assumption thatthe sectional shape of the convex tooth pin 12 b in the directionorthogonal to the reference axis is a circular arc shape; instead, asshown in FIG. 24, it is also applicable to the case where each convextooth pin 12 b has a trapezoidal shape, an involute shape, or the like.

In addition, in the above embodiments, the relationship between theconvex tooth pins 12 b of the fixed shaft 12 and the nutation concaveteeth 15 b is described; instead, it is also similarly applicable to therelationship between the convex tooth pins 13 b of the output shaft 13and the nutation concave teeth 15 c.

In addition, the above embodiments are described by setting the concaveteeth of the concave-convex gear with an intersecting axis as amachining target; instead, it is also applicable that concave teeth of aconcave-convex gear that rotates about an axis parallel to a rotationaxis of a mating gear, that is, a so-called spur gear, is set as amachining target. In this case as well, it is possible to easily andhighly accurately machine the concave teeth of the spur gear withoutusing an exclusive machine unlike the existing art.

1. A machining method for a concave-convex gear, concave teeth of theconcave-convex gear and convex teeth of a mating gear being continuouslyformed in a circumferential direction, and the concave teeth meshingwith the convex teeth of the mating gear to allow torque transmission toor from the mating gear, comprising: a trajectory extracting step ofextracting a relative movement trajectory of each convex tooth of themating gear with respect to the concave-convex gear that serves as amachining target at the time when torque is transmitted between themating gear and the concave-convex gear; and a machining step of, whenthe concave teeth of the concave-convex gear are machined on a concavetooth forming face of a disc-shaped workpiece that is the concave-convexgear on which the concave teeth have not been machined, moving at leastone of the disc-shaped workpiece and a working tool such that a relativemovement trajectory of the working tool with respect to the disc-shapedworkpiece coincides with the relative movement trajectory of each convextooth of the mating gear with respect to the concave-convex gear,extracted in the trajectory extracting step.
 2. The machining method fora concave-convex gear according to claim 1, wherein the concave-convexgear is a gear that rotates about an intersecting axis that intersectswith a rotation central axis of the mating gear.
 3. The machining methodfor a concave-convex gear according to claim 1, wherein the number ofthe convex teeth of the mating gear is different from the number of theconcave teeth of the concave-convex gear.
 4. The machining method for aconcave-convex gear according to claim 1, wherein in the trajectoryextracting step, a relative movement trajectory of a reference axis ofeach convex tooth of the mating gear with respect to the concave-convexgear is extracted, and the reference axis is an axis that is parallel toa line of intersection of a tooth thickness central plane and referenceconical surface of each convex tooth of the mating gear.
 5. Themachining method for a concave-convex gear according to claim 1, whereinthe mating gear includes a mating gear body that is integrally formedwith the convex teeth or the mating gear body that is separately formedfrom the convex teeth and that supports the convex teeth, and asectional shape of an outer peripheral surface of each convex tooth ofthe mating gear in a direction orthogonal to a reference axis of theconvex tooth is formed in a circular arc shape.
 6. The machining methodfor a concave-convex gear according to claim 5, wherein the working toolis a disc-shaped tool, and in the machining step, each convex tooth ofthe mating gear is spuriously expressed by the disc-shaped tool throughinfeed operation at multiple portions at which a central axis of thedisc-shaped tool is shifted in a tooth groove direction of acorresponding one of the concave teeth of the concave-convex gear tomachine the concave teeth of the concave-convex gear with thedisc-shaped tool.
 7. The machining method for a concave-convex gearaccording to claim 6, wherein the machining method comprises: asimulation step of performing machining simulation by moving at leastone of the disc-shaped workpiece and the working tool; and a cuttingposition calculation step of comparing a preset ideal shape model with ashape of a result of the machining simulation to calculate a position ofinfeed operation by shifting the central axis of the disc-shaped tool inthe tooth groove direction of each concave tooth of the concave-convexgear, wherein in the machining step, the concave teeth of theconcave-convex gear are machined on the basis of the position of infeedoperation, calculated in the cutting position calculation step.
 8. Themachining method for a concave-convex gear according to claim 7, whereinin the cutting position calculation step, the position of the infeedoperation is calculated so that a machining time is minimized while adeviation between the shape of the result of the machining simulationand the ideal shape model is smaller than or equal to a set permissiblevalue.
 9. The machining method for a concave-convex gear according toclaim 5, wherein the working tool is formed in a pin shape that iscoincident with or similar to an outer peripheral shape of each convextooth of the mating gear and that rotates about a pin central axis. 10.The machining method for a concave-convex gear according to claim 5,wherein the working tool is a circulating belt-shaped tool and has astraight portion in a circulating direction.
 11. The machining methodfor a concave-convex gear according to claim 1, wherein the machiningmethod comprises a coordinate conversion step of calculating a movementtrajectory of the working tool in a workpiece coordinate system bysubjecting the relative movement trajectory of each convex tooth withrespect to the concave-convex gear, extracted in the trajectoryextracting step, to coordinate conversion, and in the machining step, atleast one of the disc-shaped workpiece and the working tool is moved onthe basis of the movement trajectory of the working tool, calculated inthe coordinate conversion step.
 12. The machining method for aconcave-convex gear according to claim 11, wherein the concave-convexgear is a gear that rotates about an intersecting axis that intersectswith a rotation central axis of the mating gear, a sectional shape of anouter peripheral surface of each convex tooth of the mating gear in adirection orthogonal to a reference axis of the convex tooth is formedin a circular arc shape, a relative movement trajectory of each convextooth of the mating gear with respect to the concave-convex gear,extracted in the trajectory extracting step, is decomposed into: a firstlinear axis along which a reference position of the convex tooth of themating gear is moved in a direction orthogonal to a plane that istangent to a concave tooth forming face of the disc-shaped workpiece; asecond linear axis along which the reference position of the convextooth of the mating gear is moved in a tooth groove direction of acorresponding one of the concave teeth of the concave-convex gear in theplane that is tangent to the concave tooth forming face of thedisc-shaped workpiece; a third linear axis along which the referenceposition of the convex tooth of the mating gear is moved in a directionorthogonal to the second linear axis in the plane that is tangent to theconcave tooth forming face of the disc-shaped workpiece; a fourthrotation axis along which the reference position of the convex tooth ofthe mating gear is rotated about the first linear axis; a fifth rotationaxis along which the reference position of the convex tooth of themating gear is rotated about the third linear axis; and a sixth indexingaxis that coincides with a rotation central axis of the concave-convexgear and that indexes a rotation phase of the concave-convex gear, inthe coordinate conversion step, the relative movement trajectory of eachconvex tooth of the mating gear, expressed by the first linear axis, thethird linear axis, the fourth rotation axis, the fifth rotation axis andthe sixth indexing axis when movement of the reference position of theconvex tooth of the mating gear along the second linear axis is assumedto be performed along the third linear axis is calculated in the casewhere it is presumed that a tooth length of each convex tooth of themating gear is infinite, and in the machining step, at least one of thedisc-shaped workpiece and the working tool is moved on the basis of thecalculated relative movement trajectory.
 13. The machining method for aconcave-convex gear according to claim 11, wherein the concave-convexgear is a gear that rotates about an intersecting axis that intersectswith a rotation central axis of the mating gear, a sectional shape of anouter peripheral surface of each convex tooth of the mating gear in adirection orthogonal to a reference axis of the convex tooth is formedin a circular arc shape, a relative movement trajectory of each convextooth of the mating gear with respect to the concave-convex gear,extracted in the trajectory extracting step, is decomposed into: a firstlinear axis along which a reference position of the convex tooth of themating gear is moved in a direction orthogonal to a plane that istangent to a concave tooth forming face of the disc-shaped workpiece; asecond linear axis along which the reference position of the convextooth of the mating gear is moved in a tooth groove direction of acorresponding one of the concave teeth of the concave-convex gear in theplane that is tangent to the concave tooth forming face of thedisc-shaped workpiece; a third linear axis along which the referenceposition of the convex tooth of the mating gear is moved in a directionorthogonal to the second linear axis in the plane that is tangent to theconcave tooth forming face of the disc-shaped workpiece; a fourthrotation axis along which the reference position of the convex tooth ofthe mating gear is rotated about the first linear axis; a fifth rotationaxis along which the reference position of the convex tooth of themating gear is rotated about the third linear axis; and a sixth indexingaxis that coincides with a rotation central axis of the concave-convexgear and that indexes a rotation phase of the concave-convex gear, inthe coordinate conversion step, the relative movement trajectory of eachconvex tooth of the mating gear, expressed by the first linear axis, thesecond linear axis, the fourth rotation axis, the fifth rotation axisand the sixth indexing axis when movement of the reference position ofthe convex tooth of the mating gear along the third linear axis isassumed to be performed along the second linear axis is calculated inthe case where it is presumed that a tooth length of each convex toothof the mating gear is infinite, and in the machining step, at least oneof the disc-shaped workpiece and the working tool is moved on the basisof the calculated relative movement trajectory.
 14. The machining methodfor a concave-convex gear according to claim 11, wherein theconcave-convex gear is a gear that rotates about an intersecting axisthat intersects with a rotation central axis of the mating gear, asectional shape of an outer peripheral surface of each convex tooth ofthe mating gear in a direction orthogonal to a reference axis of theconvex tooth is formed in a circular arc shape, a relative movementtrajectory of each convex tooth of the mating gear with respect to theconcave-convex gear, extracted in the trajectory extracting step, isdecomposed into: a first linear axis along which a reference position ofthe convex tooth of the mating gear is moved in a direction orthogonalto a plane that is tangent to a concave tooth forming face of thedisc-shaped workpiece; a second linear axis along which the referenceposition of the convex tooth of the mating gear is moved in a toothgroove direction of a corresponding one of the concave teeth of theconcave-convex gear in the plane that is tangent to the concave toothforming face of the disc-shaped workpiece; a third linear axis alongwhich the reference position of the convex tooth of the mating gear ismoved in a direction orthogonal to the second linear axis in the planethat is tangent to the concave tooth forming face of the disc-shapedworkpiece; a fourth rotation axis along which the reference position ofthe convex tooth of the mating gear is rotated about the first linearaxis; a fifth rotation axis along which the reference position of theconvex tooth of the mating gear is rotated about the third linear axis;and a sixth indexing axis that coincides with a rotation central axis ofthe concave-convex gear and that indexes a rotation phase of theconcave-convex gear, in the coordinate conversion step, the relativemovement trajectory of each convex tooth of the mating gear, expressedby the first linear axis, the second linear axis, the third linear axis,the fourth rotation axis and the sixth indexing axis is calculated bydecomposing movement of the reference position of the convex tooth ofthe mating gear along the fifth rotation axis into movement along thefirst linear axis and movement along the second linear axis, and in themachining step, at least one of the disc-shaped workpiece and theworking tool is moved on the basis of the calculated relative movementtrajectory.
 15. The machining method for a concave-convex gear accordingto claim 11, wherein the concave-convex gear is a gear that rotatesabout an intersecting axis that intersects with a rotation central axisof the mating gear, a sectional shape of an outer peripheral surface ofeach convex tooth of the mating gear in a direction orthogonal to areference axis of the convex tooth is formed in a circular arc shape, arelative movement trajectory of each convex tooth of the mating gearwith respect to the concave-convex gear, extracted in the trajectoryextracting step, is decomposed into: a first linear axis along which areference position of the convex tooth of the mating gear is moved in adirection orthogonal to a plane that is tangent to a concave toothforming face of the disc-shaped workpiece; a second linear axis alongwhich the reference position of the convex tooth of the mating gear ismoved in a tooth groove direction of a corresponding one of the concaveteeth of the concave-convex gear in the plane that is tangent to theconcave tooth forming face of the disc-shaped workpiece; a third linearaxis along which the reference position of the convex tooth of themating gear is moved in a direction orthogonal to the second linear axisin the plane that is tangent to the concave tooth forming face of thedisc-shaped workpiece; a fourth rotation axis along which the referenceposition of the convex tooth of the mating gear is rotated about thefirst linear axis; a fifth rotation axis along which the referenceposition of the convex tooth of the mating gear is rotated about thethird linear axis; and a sixth indexing axis that coincides with arotation central axis of the concave-convex gear and that indexes arotation phase of the concave-convex gear, in the coordinate conversionstep, the relative movement trajectory of each convex tooth of themating gear, expressed by the first linear axis, the second linear axis,the third linear axis, the fifth rotation axis and the sixth indexingaxis when the fourth rotation axis is brought into coincidence with thesixth indexing axis is calculated, and in the machining step, at leastone of the disc-shaped workpiece and the working tool is moved on thebasis of the calculated relative movement trajectory.
 16. A machiningdevice for a concave-convex gear in which concave teeth and convex teethare continuously formed in a circumferential direction and the concaveteeth mesh with convex teeth of a mating gear to allow torquetransmission to or from the mating gear, characterized by comprising:trajectory extracting means for extracting a relative movementtrajectory of each convex tooth of the mating gear with respect to theconcave-convex gear that serves as a machining target at the time whentorque is transmitted between the mating gear and the concave-convexgear; and machining means for, when the concave teeth of theconcave-convex gear are machined on a concave tooth forming face of adisc-shaped workpiece that is the concave-convex gear on which theconcave teeth have not been machined, moving at least one of thedisc-shaped workpiece and a working tool such that a relative movementtrajectory of the working tool with respect to the disc-shaped workpiececoincides with the relative movement trajectory of each convex tooth ofthe mating gear with respect to the concave-convex gear, extracted bythe trajectory extracting means.